14 problems

Consider $N$ indistinguishable spinless fermions in a three-dimensional box of volume $L^3$, with density $\rho=N/L^3$, Hamiltonian $H_N$, and ground-state energy…

Consider the momentum distribution of the ground state of the interacting Fermi gas, and let the Kohn–Luttinger effect denote the superconducting instability expected to smooth the…

Let $V$ be an interaction potential for the Fermi gas, and let the Fermi momentum denote the radius of the Fermi sphere in the isotropic case. Universality conjecture. The Fermi mo…

Huang–Yang conjecture. The next correction is the Huang–Yang term, of order $a_s^2\rho^{7/3}$. This conjecture concerns the next term beyond the kinetic-energy and first interactio…

RPA correlation-energy conjecture. Even with attractive potentials, the RPA formula for the correlation energy applies as long as the logarithm in $E_N^{\operatorname{RPA}}$ does n…

Let $\hat{V}:\mathbb{Z}^3\to\mathbb{R}$ be non-negative and compactly supported. Let $k_F>0$ be the Fermi momentum, let … be the number of particles, set $\hbar=N^{-1/3}$, and defi…

Consider the non-interacting Fermi gas of $N$ particles with one-particle density matrix $\rho$, and take the non-conventional large-$N$ limit in which the Fermi gas makes contact…

Let $Z(N,\hbar)$ be the canonical partition function of the non-interacting Fermi gas associated with the quantized mirror curve of a genus-one toric Calabi--Yau manifold, where…

Airy universality conjecture. In any Chern–Simons–matter theory which displays the $N^{3/2}$ behavior for the strict large-$N$ limit of its partition function, the leading term of…

TBA-like equations conjecture. The function $R(\theta\mid\kappa)$ can be obtained by using TBA-like equations. This conjecture was proved in the cited work, so its database status…

Gaudin's conjecture. As $\gamma\to0$, the Fermi contribution to the ground-state energy satisfies

Let $\nu_j^\pm({\bf k})$ be the thermodynamic-limit $j$th shell in the even or odd sector of the finite-volume interacting Fermi-gas Hamiltonian, and define … Here…

Let $H^L$ be the finite-volume Hamiltonian of an interacting Fermi gas in a periodic box, with ground-state energy $E^L$. For momentum ${\bf k}$, let $\epsilon^\pm({\bf k})$ denote…

Consider a homogeneous interacting Fermi gas in the thermodynamic limit, treated using the Hartree–Fock–Bogoliubov approximation. Let the resulting quasiparticle representation hav…